Why should you balance the propellers on your quadcopter or multicopter? The answer is simple, to reduce vibration. Vibration can be a villain, it can cause your multicopter to wobble while hovering, cause the "jello effect" when shooting aerial video and increase the wear on bearings greatly reducing the life of your motors. If you are serious about fpv racing, then balancing your propellers is a must and will allow you to run higher (or tighter) pids on your fpv racer.
To balance your propellers, there are two types of balancing techniques:
1) Static Balancing
1) Dynamic Balancing
So what is static and dynamic balancing? Static balancing is performed on a stationary propeller and is a very simple procedure. Dynamic balancing is done together with a mated motor while the propeller and motor is running. This procedure requires both software and a specially designed rig to hold and run the propeller/motor combination and measure the offset or out of balance condition to determine where to place the balance weights. Of the two, static balancing is the more widely used technique, not necessarily because of accuracy but more because simple static balancers are more readily available to the general public.
To balance the propellers for your quadcopter or multicopter (multirotor) you will need a propeller balancer which you have either made or purchased. Purchased units are very inexpensive and are probably the way to go since you more than likely are not going to build your own for less. But what you will have to make is a simple base plate to set your balancing unit on. This base plate is nothing more than a small square piece of plywood or pressboard, with a wood screw in each corner to allow for levelling of the plate (below photo).
Using a small level ensure that the base plate is absolutely level (front to back, side to side and diagonally across). Adjustments can be done by turning the wood screws appropriately. Once level, place the propeller balancer on the base plate. Depending upon the style of balancer that you have, you may have to check that it is actually square to the base (some have removable legs and don't always sit square in the balancer itself). With that done mount the propeller on the holder and set it in place on the propeller balancer. (A note worthy point is to make sure that your work space is free from any air movement that may cause the propeller to move on the balancer, which could give you a false indication of balance or out of balance.)
If the propeller is out of balance, one side will be lower than the other, which is quite often the case. To add weight to the lighter side you can simply add some nail polish. The nail polish should be applied to the underside of the propeller and at the tip (above photo). By applying the nail polish to the tip of the propeller as a counter weight, you will actually use less because you are taking advantage of the principle of leverage. Keep applying the nail polish until you have achieved a balanced condition. In some cases, you may actually have to work from side to side but don't be discouraged, just work diligently and with patience!